Home > Statistical Methods calculators > Fitting a second degree parabola - Curve fitting calculator

Solve any problem
(step by step solutions)
Input table (Matrix, Statistics)
Mode :
SolutionHelp
Solution will be displayed step by step (In 2 parts)
Solution
Find Fit second degree parabola equation {{1996,1997,1998,1999,2000},{40,50,62,58,60}}

Solution:
Your problem `->` Fit second degree parabola equation {{1996,1997,1998,1999,2000},{40,50,62,58,60}}


The equation is `y = a + bx + cx^2` and the normal equations are

`sum y = an + b sum x + c sum x^2`

`sum xy = a sum x + b sum x^2 + c sum x^3`

`sum x^2y = a sum x^2 + b sum x^3 + c sum x^4`


`X``y``x = X - 1998``x^2``x^3``x^4``x*y``x^2*y`
199640-24-816-80160
199750-11-11-5050
199862000000
19995811115858
20006024816120240
------------------------
999027001003448508


Substituting these values in the normal equations
`270=5a+0b+10c`

`48=0a+10b+0c`

`508=10a+0b+34c`


Solving these 3 equations using inverse matrix method,
Here `5a+10c=270`
`10b=48`
`10a+34c=508`

Now converting given equations into matrix form
`[[5,0,10],[0,10,0],[10,0,34]] [[a],[b],[c]]=[[270],[48],[508]]`

Now, A = `[[5,0,10],[0,10,0],[10,0,34]]`, X = `[[a],[b],[c]]` and B = `[[270],[48],[508]]`

`:. AX = B`

`:. X = A^-1 B`

`|A|` = 
 `5`  `0`  `10` 
 `0`  `10`  `0` 
 `10`  `0`  `34` 


 =
 `5` × 
 `10`  `0` 
 `0`  `34` 
 `+0` × 
 `0`  `0` 
 `10`  `34` 
 `+10` × 
 `0`  `10` 
 `10`  `0` 


`=5 xx (10 × 34 - 0 × 0) +0 xx (0 × 34 - 0 × 10) +10 xx (0 × 0 - 10 × 10)`

`=5 xx (340 +0) +0 xx (0 +0) +10 xx (0 -100)`

`=5 xx (340) +0 xx (0) +10 xx (-100)`

`= 1700 +0 -1000`






Solution provided by AtoZmath.com
Any wrong solution, solution improvement, feedback then Submit Here
Want to know about AtoZmath.com and me
  
 

Share with your friends, if solutions are helpful to you.
 
Copyright © 2019. All rights reserved. Terms, Privacy